Temperature Modeling in a Coke Furnace with an Improved RNA-GA

Article pubs.acs.org/IECR

Temperature Modeling in a Coke Furnace with an Improved RNA-GA Based RBF Network Ridong Zhang,†,§ Jili Tao,*,‡ and Furong Gao§ †

Information and Control Institute, Hangzhou Dianzi University, Hangzhou, 310018 Zhejiang, P R China Ningbo Institute of Technology, Zhejiang University, Ningbo, 315100 Zhejiang, P R China § Department of Chemical and Biomolecular Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong ‡

ABSTRACT: The temperature modeling of the coke furnace in industrial coke equipment is not very easy due to disturbances, nonlinearity, and switches of coke towers. For characterizing the temperature dynamics in a coke furnace, a more comprehensive RBF modeling method is presented focusing on improving the modeling precision and simplifying the model structure simultaneously. An improved RNA-GA is then utilized to optimize both the structure and parameters of the RBF neural network. RNA encoding and evolution operations, particularly pruning operation and enumerative method, are introduced, and fitness function is designed to obtain the satisfactory modeling performances. The industrial data is used to demonstrate the effectiveness and feasibility of the proposed modeling strategy.

1. INTRODUCTION Coking has received considerable attention due to its advantage of enhancing economic benefits.1,2 The temperature control in the coke furnaces is not very easy because of the interactions in the whole coke unit.3 Modeling is quite important for advanced controller design but is difficult with nonlinear characteristics, time delay, and other various disturbances, such as feeding quantity, feeding temperature, fuel amount, etc. The temperature in a coke unit using one-order inertia plant with time delay was already studied.4 However, the model is constrained by its specification of the operation condition, and it has low modeling precision. One promising method to overcome these difficulties is to construct a temperature plant model by using neural networks. Neural networks (NN) are data based models, and a properly trained neural network can be used to predict output values for new input data. For their good learning ability, NN are widely applied to the modeling of the nonlinear processes.5,6 A radial basis function (RBF) network was first proposed by Broomhead and Lowe in 1988 in accordance with the partial response character of neuron. It is a powerful regression tool with better approximation capabilities, simpler network structures, and faster learning algorithms than multilayer perception networks and has been applied in many fields.7−9 When RBF neural networks (RBFNNs) are used to develop temperature forecasting models, the learning algorithm of RBFNN is critical. The essential of the learning algorithm is to determine the network structure and its parameters. Different learning algorithms have great influence on the performance of the derived RBFNN models. If the number of input layers and hidden nodes used in the RBF network is too large, it may lead to overfitting. On the contrary, if the number of input layers and hidden nodes is too small, it may fail to map input patterns into output patterns. The best generalization performance may be obtained via a compromise between the conflicting requirements of reducing prediction error while simultaneously © 2014 American Chemical Society

reducing model complexity. This trade-off highlights the importance of optimizing the complexity of the model in order to achieve the best generalization. The inclusion of the structure selection for the RBF modeling is desirable but results in a rather difficult problem, which cannot be easily solved by the standard optimization methods. Studies regarding learning algorithms and determination of the network structure have been proposed in the literature. A simple sequential learning algorithm for RBF neural networks is proposed in ref 8, which is referred to as the RBF growing and pruning algorithm. Du et al.10 proposed a multioutput fast recursive algorithm (MFRA), formulating the construction of an RBF network as a linear parameters problem. Han et al.11 presented a flexible structural Radial Basis Function (FS-RBF) neural network, which can change its structure dynamically in order to maintain the prediction accuracy. Most previous algorithms become inefficient with too large of a search space and tend to be trapped into the local minimum. Recently, an interesting alternative for solving this complicated problem can be offered by genetic algorithms (GAs),12 and it has been successfully utilized for the selection of the number of RBF hidden neurons and the structure and parameters of RBF networks.13,14 Although GA would have its ability to do global searching, it is challenged by its weak local-search capability and premature convergence. As such, some biological operations at the gene level are effectively adopted in the existing GA, and the global searching speed can be largely improved.15,16 In this paper, an RBFNN model optimized by improved RNA-GA is proposed for forecasts of temperature in a coke furnace. The improved RAN-GA learning algorithm, which Received: Revised: Accepted: Published: 3236

August 22, 2013 February 3, 2014 February 8, 2014 February 8, 2014 dx.doi.org/10.1021/ie4027617 | Ind. Eng. Chem. Res. 2014, 53, 3236−3245

Industrial & Engineering Chemistry Research

Article

Figure 1. Overall flow of coke unit.

operated through batch mode, i.e., when one is full, the other replaces it. There are disturbances such as the heat exchange in the fractionating tower, the switch of coke towers T101/5 and T101/6, and the random switch time of the coke towers, which pose continuous disturbances on the outlet temperature.

consists of the simultaneous optimization of architecture and parameters, is a novel one. Two properties are contained in the proposed optimal algorithm. The first is that improved RNAGA operators and the pruning operation of candidates for hidden layers and parameters of Gaussian functions are introduced to efficiently optimize the network, and the structure of input layers is solved by the enumerative method. The second is that its fitness function considers both forecasting capability and structure complexity of the RBF neural network. These two properties are expected to be helpful for developing the RBF network. In order to assess the ability of the proposed model, the product data is yielded by actual applications. Furthermore, to demonstrate the superiority of the proposed model, comparisons between the forecasts of the proposed model and those results from other RBFNN models are presented.

3. IMPROVED RNA-GA BASED RBF MODELING An RBF neural network has a simple neural network structure in terms of the direction of information flow. Since the performance of an RBF neural network is heavily dependent on its architecture, research has focused on self-organizing methods that can be used to design the architecture of threelayer RBF neural networks, such as k-means clustering,18 the nearest neighbor clustering,19 etc. k-means clustering is a most widely used partitioning method suitable for large amounts of data. It finds a partition in which objects within each cluster are as close to each other as possible and as far from objects in other clusters as possible. When used in selecting the centers of RBF, the number of input and hidden neurons, the width of RBF need to be set in advance. In order to design the structure, the centers, and the width of the RBF neural network automatically, an improved RNA-GA tuning strategy is used. This strategy changes the topology of the RBF neural network by RNA encoding, decoding, and pruning operation. Furthermore, an objective function is proposed to consider both the structure complexity and the

2. THE COKE UNIT The detailed process flow of the considered coke unit can be referred to as in ref 17 (also see Figures 1 and 2). Here furnace (F101/3) is taken as an example. There are typically three stages of this operation. First, two branches of residual oil (FRC8103, FRC8105) are preheated in the furnace and then exchange heat with gas oil in the fractionating tower (T102). Second, two branches of circulating oil (FRC8107, FRC8108) in the fractionating tower flow into the furnace to be heated to about 495 °C. Finally, the circulating oil goes into the coke towers (T101/5,6) for coke removing. The coke towers are 3237

dx.doi.org/10.1021/ie4027617 | Ind. Eng. Chem. Res. 2014, 53, 3236−3245


Article

Figure 2. Overall flow of coke furnace. nr

generalization capability in the RBF neural network training process. 3.1. Radial Basis Function Neural Network. This section will give the nonlinear modeling procedure through RBF neural network (RBFNN). A schematic of the RBF network with n inputs and a scalar output is depicted in Figure 3, which shows the structure of a basic RBF network consisting of one input layer, one output layer, and one hidden layer. Such a network implements a mapping: Rn → R according to

y(x) =

⎛ || x − c || ⎞ i ⎟ 2 ⎝ σi ⎠

∑ ωiϕ⎜ i=1

(1)

where x = (x1, x2···, xn) is of n inputs, only used to connect the network to its environment, y denotes the output of the network, ci ∈ Rn denotes the center vector of the ith hidden neuron, ϕ(·) is a given Gaussian function, ∥·∥ denotes the Euclidean distance between x and ci, ωi is the connecting weight between the hidden neuron and the output layer, σi is the width of Gaussian function, 1 ≤ i ≤ nr, and nr is the number of hidden layer nodes. By providing nr outputs of a hidden layer, and the corresponding desired output y(t) for t = 1 to M, the weights can be determined by using the recursive least-squares (RLS) method. However, the number of input and hidden layers, the parameters σi and ci, must be carefully considered in order to obtain both the good approximation capability and simple structure of RBFNN. Since the choice of input layers is finite, i.e., 2 ≤ n ≤ 5, it can be enumerated in the optimization process. The structure of x(t) is then constructed by 6 combinations of system input (u)

Figure 3. The RBFNN structure. 3238



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Figure 4. Quanternary encoding for Cl.

Figure 5. Example of the crossover operation.

and previous system output (y). For example, if n is 2, x(t) is [u(k),y(k-1)]; if n is 3, x(t) is [u(k), u(k-1), y(k-1)] or [u(k), y(k-1), y(k-2)]; if n is 4, x(t) is [u(k), u(k-1), y(k-1), y(k-2)]; if n is 5, x(t) is [u(k), u(k-1), y(k-1),y(k-2), y(k-3)] or [u(k), u(k1), u(k-2),y(k-1), y(k-2)]. The hidden layer of RBFNN is to be optimized by improved RNA-GA. 3. 2. Improved RNA-GA for RBFNN. RNA-GA is an optimization algorithm based on DNA computing with good optimization quality and efficiency.15 Depending on the features of the problem’s solution space, there is a great range of choices on the fitness functions, the encoding/ decoding method, and the genetic operations, and all of these factors affect the efficiency of GA. This work is focused on the optimization of the RBF network by the improved RNA-GA. 3.2.1. Encoding and Decoding Method. The structure of the lth chromosome is shown as follows ⎡ cl cl ⎢ 1,1 1,2 ⎢ l l ⎢ c 2,1 c 2,2 ⎢ ⋮ ⋮ ⎢ Cl = ⎢ l l c c ⎢ nr ,1 nr ,2 ⎢ 0 0 ⎢ ⋮ ⋮ ⎢ ⎢⎣ 0 0

··· c1,l n σ1 ⎤ ⎥ ⎥ l ··· c 2, n σ2 ⎥ ⋱ ⋮ ⋮⎥ ⎥ ··· cnl r , n σnr ⎥ ⎥ 0 0 0⎥ ⎥ ⋮ ⋮ ⋮⎥ 0 0 0 ⎥⎦

σj =

1≤j≤n

(4)

where Q is the integer decoded by quaternary code with length L, L is set to 6 in Figure 4, xj,min and xj,max are the minimum and maximum values of input variables given in the problem, and wmax is the maximum value of width for Gaussian basis function. 3.2.2. Fitness Function. The training procedures using RNAGA are processed in two steps. First, the network structure and the basis function parameters are determined by chromosomes in one population. Second, the final-layer weights are determined by the recursive least-squares method. Since IRNA-GA is a random search algorithm, the linear system output may be ill-conditioned, and the ordinary least-squares method cannot be used in the optimization process. In every generation of RNA-GA, the calculation of the output weights completes the formulation of N RBFNN, which can be represented by the pairs (C1, ω1), (C2, ω2),···(CN, ωN). To obtain good generalization ability of RBF networks, the data are divided into 3 groups: one group of data (X1, Y1) is used to calculate the final-layer weights, the second group (X2, Y2) is utilized to evaluate the produced RBFNN in each generation, and the third group (X3, Y3) is used to verify the performance of the best RBFNN. This scheme incorporates a testing procedure into the training process and guarantees good generalization performance of RBFNN. However, to obtain better approximation capability with a simpler structure and avoid neural network overfitting, the objective function considering both approximation capability and structure complexity is shown as follows:

(2)

where l = 1, 2,···N, N is the size of the population, nr is produced randomly between 1 and D, D is the maximum number of hidden neurons, the rows below nr are set to zeros, n is the number of input layers and composed of system inputs (u) and outputs (y). There are totally D × (n + 1) real parameters to be optimized in the RBFNN, and the elements of Cl are coded by 0123 as shown in Figure 4, which means one chromosome is made up of D × (n + 1) × L RNA genes. The chromosome can be decoded by the following equation cij = xj ,min +

Q wmax 4L − 1

N1

J(Ci , ωi ) =

N2

∑ |Y1(t ) − Y1̂ (t )|2 + ∑ |Y2(t ) − Y2̂ (t )|2 t=1

+ λ(nr + n)

t=1

(5)

This criterion expresses a compromise between the cost of modeling errors and the complexity of network structure, λ is a coefficient between 0 and 1, and the bigger λ is, the more important the number of input layers and hidden nodes. 3.2.3. Operators in RNA-GA. Li et al.20 summarized all possible operations of the DNA system, such as elongation

Q ·(xj ,max − xj ,min) 1 ≤ i ≤ nr , 4 −1 L

(3) 3239



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change. The changing curve with the evolution generation of pm is shown in Figure 6. The coefficients of eq 7 are selected as follows: a0 = 0.02, b0 = 0.2, g0 = G/2, aa = 20/G. Let G be 1000, and the curve of pm is shown in Figure 6.

operation, deletion operation, absent operation, insertion operation, translocation operation, transformation operation, and permutation operation, etc. In addition to selection, crossover, and mutation operators, appropriate DNA operations adopted by RNA-GA may improve the optimal results of RBFNN modeling. (1). Selection Operator. A set of individuals from the previous population must be selected for reproduction. This selection depends on their fitness values. Individuals with bigger fitness values will more probably survive. There exist different types of selection operators, and in this work the roulette wheel method is applied. The probability of an individual being selected, P(Cl), is given by

P(Cl ) =

f (Cl ) N ∑l = 1 f (Cl )

(6)

where f(Cl) is the fitness value of individual Cl, which is obtained by 1/J(Cl, wl). The roulette wheel is placed with N equally spaced pointers. A single spin of the roulette wheel will simultaneously pick N members of the next population. (2). Crossover Operator. The crossover operator is applied after selection and produces a new structure and the parameters of RBFNN. Not all of the selected individuals are crossed over; this depends on the crossover probability, pc. Crossover operation is executed between current chosen individual Cl and the next individual Cl+1 and yields the offspring chromosomes C′l , C′l+1. Since the input number n is fixed during the one optimization process, the procedure is demonstrated with the example presented in Figure 5, which contains a scheme of the multipoint crossover; there are totally D × (n+1) crossover operations. The operator will be prone to produce more hidden neurons, e.g., after the crossover of cnr+1,n of Cl and cnr+1,n of Cl+1, the new nonzero chromosomes are produced, and the number of hidden nodes in Cl is increased. (3). Mutation Operator. To have a better exploration of the search space, the mutation operator is carried out. Because there exist four elements (0123) in the RNA sequence, the mutation of the nucleotide base is relatively complex. Three main operations on a single RNA sequence, i.e., reversal, transition, and exchange, are adopted. The reversal operator makes 0 ↔ 2, 1 ↔ 3, the transition operator makes 0 ↔ 1, 2 ↔ 3, and the exchange operator makes 2 ↔ 1, 0 ↔ 3. When the element of an individual is mutated with a probability pm, three mutation operators are executed simultaneously. This will generate more than N individuals after mutation operators. The population size will remain invariant by the selection operator in the next generation. The mutation probability is critical and generally small since too large of a mutation probability makes the RNA-GA random search algorithm. At the beginning stage of evolution, a larger probability of mutation is assigned to RNA nucleotide bases, so the larger feasible region is explored. When the region of the global optimum is found, the mutation probabilities are decreased to prevent better solutions from disruption. Accordingly, the mutation probability pm is described as follows pm = a0 +

Figure 6. Mutation probability decreasing with g increasing.

After calculating the mutation probability in terms of eq 7, L × N decimal fractions between 0 and 1 are produced compared with the above probability. If the mutation probability is larger than the corresponding probability in Figure 6, 3 RNA mutation operators are executed sequentially. (4). Pruning Operator. Since the chromosomes are generated randomly, the effectiveness of every hidden neuron is evaluated considering the active firing (AF) value of the hidden neurons, which is described by the following equation11 Afi = ρe− || x − ci ||

(i = 1, 2, ···, nr )

(8)

where Af i is the active firing value of the ith hidden neuron, and ρ is a positive constant, which is set as 100. When Af i is less than the active threshold Afo (0.05 < Afo < 0.3), the ith hidden neuron is not the active neuron. The number of hidden neurons (nr) will be decreased, the corresponding ci is moved to the last location of cnr, and its values of chromosomes are then set to zeros. 3.2.4. The Process of Optimization. The processes of function evolution, selection, crossover, mutation, and pruning are described for improved RNA-GA in the following steps: Step 1: Generate an input layer with 2 input nodes and construct the structure of x(t), x(t) = [u(k),y(k-1)]. Step 2: Generate randomly N quaternary chromosomes with length of D × (n+1) × L in the search space, where N is the population size. Step 3: Decode and compute the performance J of each of the individual. Step 4: Select the chromosomes (parents) to generate N new chromosomes (children) of the next generation according to selection operator. The commonly used tournament selection for ⟨3N/4⟩ individuals and the worst ⟨N/4⟩ individuals are directly inherited to keep population diversity. Here ⟨·⟩ is to ceil the elements to the nearest integer. Step 5: Select 1 point randomly in L quaternary genes, and totally D × (n+1) points are generated as shown in Figure 5;

b0 1 + eaa(g ‐ g0)

ϕ (x )

i , n ∑i =r 1 ϕi(x)

(7)

where a0 denotes the initial mutation probability of pm, b0 is the variation range of mutation probability, g is the evolution generation, g0 decides the generation where th greatest change of mutation probability occurs, and aa denotes the speed of 3240



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Figure 7. a. Input FRC8105 and output TRC8105 for north side primary channel modeling. b. Input FRC8105 perturbation and output TRC8105 for north side disturbances modeling. c. Input FRC8103 and output TRC8103 for south side primary channel modeling. d. Input FRC8103 perturbation and output TRC8103 for south side disturbances modeling.

Table 1. Simulation Results Comparison with 2 Different Methods TRC8105

TRC8105 disturbances

TRC8103

TRC8103 disturbances

methods

n

nr

e1

n

nr

e1

n

nr

e1

n

nr

e1

IRNAGA k-means

4 4

32 38

0.0094 0.0584

3 3

38 38

0.0439 0.3245

4 4

31 38

0.0305 0.2707

3 3

28 38

0.0813 0.0866

4. TEMPERATURE MODELING OF A PRACTICAL DELAYED COKING PROCESS

exchange the codes of parents selected in step 4. Repeat this for all the pc × N/2 pairs of parents. Step 6: Execute 3 RNA mutation operators successively once the random number is less than the probability of mutation in eq 7; this step may generate the individuals more than N. Step 7: If the number of individuals is more than N, then the pruning operator is implemented in the new individuals to improve the quality of RBFNN, else the pruning operator is not carried out. Step 8: Repeat steps 3 to 7 until a termination criteria is met. The criteria is the maximal number of evolution (G). Moreover, elitism, the inclusion of the best current set in the next population, is used throughout the optimization process. Step 9: Increase the number of input layers and reconstruct the x(t); repeat steps 2 to 8. Choose the best RBFNN in terms of the value of objective function by using test data.

Advanced temperature control is critical for coke unit, and the first important issue is system modeling. In this work, RBFNN optimized by an improved RNA-GA and enumerative method is used to complete the north and south sides of the temperature model and its main disturbances in the coking furnace. The experimental data are gathered from an industrial coking unit of a refinery controlled by DCS CS3000. The temperature is measured by thermocouple with the measuring precision 1.5 rate, and the flow rate is measured by mass flow meter. To guarantee the modeling precision and let the administrator conveniently analyze the process data, the sampling period of 5 s is selected in the database named PAI, and 2 digits after the decimal point are maintained in the sampling data. 1350 samples are obtained from the PAI database of the control 3241



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Figure 11. RBFNN model output for TRC8105 using the k-means method.

Figure 8. Modeling error of TRC8105 using IRNAGA.

Figure 9. RBFNN model output for TRC8105 using IRNAGA. Figure 12. Modeling error for TRC8105 disturbances using IRNAGA.

Figure 10. Modeling error of TRC8105 using the k-means method. Figure 13. RBFNN model output for TRC8105 disturbances using IRNAGA.

system. Each sample contains the measurement of 4 inputs and 4 outputs, which includes the north side primary channel model of the outlet temperature (TRC8105) and the input temper3242



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Figure 17. RBFNN model output for TRC8103 using IRNAGA.

Figure 14. Modeling error of TRC8105 disturbances using the kmeans method.

Figure 18. Modeling error of TRC8103 using the k-means method. Figure 15. RBFNN model output for TRC8105 disturbances using the k-means method.

Figure 19. RBFNN model output for TRC8103 using the k-means method.

ature set-point, its disturbance channel model of the perturbation of FRC8105 and its corresponding temperature of TRC8105, the south side primary channel model of the

Figure 16. Modeling error of TRC8103 using IRNAGA.

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Figure 20. Modeling error of TRC8103 disturbances using IRNAGA.

Figure 23. RBFNN model output for TRC8103 disturbances using the k-means method.

outlet temperature (TRC8103) and the input temperature setpoint, and its disturbance channel model of the perturbation of FRC8103. Four groups of input and output data are shown from Figure 7a to Figure 7d, where the x-axis is the number of samples, the y-axis labeling on the left is the system temperature output, and the y-axis labeling on the right is the system flow output. There are totally 4 RBFNNs to model the above temperature variables, and the system input (u) and output (y) of the input layer x(t) in each RBFNN is variable according to the different plants. The proposed methodology is compared to the k-means method, which is used to train RBF network centers; the pruning operator is also applied, and final-layer weights are derived by using the RLS method; the number of input layers is the same as the optimized RBFNN. The maximal number of RBFNN hidden neurons is set at 38, which is also gained according to the number of hidden nodes optimized by IRNAGA. All the gathered 1350 samples are divided into 3 groups. The first 450 samples are selected as the training set, and the intermediate 450 samples are used to verify the generalization capability of RBFNN; the remaining 450 samples are used as the final testing set. Based on the data of 3 groups, the improved RNAGA (IRNAGA) is employed to optimize the structure and parameters of RBFNN by minimizing eq 5. Here, the parameters of the improved RNAGA are set as follows: population size N = 60, evolution generation limitation G = 1000, individual length L = n × D, the operator probability pc = 0.6, pm is dynamic changing according to eq 7, the active threshold Afo is set as 0.1, λ is set to 0.3, and wmax is set to 120. To examine the generalization ability of the constructed model, the trained RBFNN is used to predict the coke temperature yield of the testing samples, which are not included in the training data. Furthermore, for validation of the effectiveness of the proposed random optimization algorithm, RBFNN is trained for 10 times. In each time, the parameters of IRNAGA and the data set are kept invariant. The best results are listed in Table 1, where e1 is the Root Mean Squared Error (RMSE) of the testing data. From Table 1, the best results of IRNAGA can obtain better prediction precision than the results using the k-means method in terms of the Root Mean Squared Error e1. Moreover,

Figure 21. RBFNN model output for TRC8103 disturbances using IRNAGA.

Figure 22. Modeling error of TRC8103 disturbances using the kmeans method.

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RBFNN using IRNAGA can obtain a smaller error with fewer hidden nodes for 4 groups of the testing data than the k-means method. Even though the RMSE of the TRC8103 disturbance model using IRNAGA is similar to that of the k-means method, 28 hidden nodes by IRNA-GA is much less than 38 hidden nodes using the k-means method. It can be seen that all of the best results in 10 runs are superior to the k-means method, since the RBFNN with fewer nodes gains better generalization capability. The structure of RBFNN and modeling precision are optimized greatly after running IRNAGA. To reflect the prediction accuracy of the established model, the comparisons of predicted temperature and measured temperature on the testing set for the main channels of the north side and the south side (TRC8105, TRC8103) and their disturbance channels are given in Figures 8−23 and Table 1, respectively. Figure 8 shows the modeling error of TRC8105 using the IRNAGA, while the corresponding prediction error is shown in Figure 9. Figure 11 shows the fitting curve of prediction values and real value using the k-means method, and the estimation errors are depicted in Figure 10. Comparing Figure 8 with Figure 10, the maximal modeling error obtained by the k-means method is several times more than that obtained by IRNAGA. The same results can be observed comparing with the modeling error of TRC8103 and their disturbance models, as shown in Figure 13, Figure 15, Figure 17, Figure 19, Figure 21, and Figure 23. From Figure 8 to Figure 23, it can be concluded that the proposed approach has managed to sustain the error to considerably smaller values by a simpler network structure.

In this study, temperature models of delayed coke furnaces are constructed by using an RBF neural network and an improved RNAGA. Due to the ability of adequately approximating to the complicated systems, RBF neural networks are applied to construct the temperature models by using the data gathered from industrial equipment. To improve the approximation and generalization performance, an improved RNAGA is developed to optimize the Neural Network structure and its corresponding parameters of basis functions. A pruning operator and an enumerative method of input layers are also designed to simplify the RBFNN structure. The simulation results show that the constructed RBFNN model optimized by IRNAGA can obtain good prediction accuracy with a relatively simple network structure.

AUTHOR INFORMATION

Corresponding Author

*Phone: +86-574-88130021. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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5. CONCLUSION

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ACKNOWLEDGMENTS

The authors acknowledge Hong Kong, Macao, and Taiwan Science & Technology Cooperation Program of China (Grant No. 2013DFH10120), National Natural Science Foundation of China (Grant No. 61273101), and China Postdoctoral Science Foundation Funded Project (Grant No. 2013T60590). 3245


Temperature Modeling in a Coke Furnace with an Improved RNA-GA

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